RBS was bailed out in 2008 and the government still holds all of its 81 per cent shareholding (Source: Getty)

George Osborne is considering selling some RBS shares this year even if the taxpayer makes a loss, as he runs out of patience with the bailed-out bank.

The chancellor is understood to be weighing up the options for the future of the state-backed lender over the next two weeks.

He has been buoyed by the successful sale of more than half of the taxpayers’ stake in Lloyds at a profit, and hopes to sell the rest of the lender over the coming months.

By contrast, RBS remains a loss-making thorn in the government’s side. The Treasury still holds an 81 per cent stake in RBS.

To make a profit, the government would need to sell at a share price of above 502p. On Friday the stock closed at 352.4p.

However, the shares did rise 6.1 per cent on the news that the Conservatives won the election, potentially giving the chancellor a small excuse to argue he is getting a relatively good price for the stock.

In contrast to Lloyds, RBS’ share price has been held down in part by more serious government meddling, which dissuaded investors from backing the bank. A share sale could indicate to those shareholders that the Treasury is at last backing off.